We decompose two implementations of Shor’s algorithm for prime factorization into universal gate units at the logical level and predict the number of physical qubits and execution time when surface codes are used. Logical qubit encoding using a rotated surface code and logical qubits with all-to-all connectivity are assumed. We express the number of physical qubits and execution time in terms of the bit length of the number to be factorized and error rate of the physical quantum gate. We confirm the relationship between the number of qubits and the execution time by analyzing two algorithms using various bit lengths and physical gate error rates.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No.2019R1A2C2010061). This work was supported by Institute for Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [No. 2020-0-00014, A Technology Development of Quantum OS for Fault-tolerant Logical Qubit Computing Environment]
© 2022, The Author(s).
- Quantum algorithm
- Quantum computation
- Quantum error correction
- Quantum gates
- Quantum resource analysis
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Statistical and Nonlinear Physics
- Theoretical Computer Science
- Signal Processing
- Modelling and Simulation
- Electrical and Electronic Engineering